2005 Speed Triple Rear Caliper

http://www.motorcyclespecs.co.za/bikes/triumph 2.htm

http://www.worldoftriumph.com/triumph-motorcycle-parts.html

https://www.triumphparts.gbr.cc/index.php/31/515041/


Get the caliper off and on the bench, and give it a go perhaps if you push the pin the thread may engage.
Heres some sites for your colletion.

 

If you are intent on keeping the caliper then I’d be inclined to remove it from the bike and use some penetrating oil on the threads leaving it to soak in and reapplying a couple of times. If you are able to then push the pads back in and with a pair of vice grips on the pins rotate them instead of trying to get an Allen key to fit. You could always force an Allen key in, the next size up, and try that to remove the pins. If it still resists then heat the alloy of the caliper with a hot air gun and perhaps use some freeze spray on the pins that should expand the alloy and contract the steel pin allowing removal. If you get them out inspect the threads carefully and consider replacing the seals and maybe even the pistons. Alternatively the bottom of the three links isn’t to badly priced for a new caliper.

 

You may get away with tapping in a tight fitting torx bit with a hammer then remove the bolts after giving them a good dose of 50/50 atf & acetone or pb blaster releasing oil

 

I made up Allen keys slightly bigger at 5.1 mm perfect fit.
If you can' undo send to me and ill remove them for you.
Made up a key for Dozers Dad.
Even a new key is 4.95mm and is a bad fit.